Enjoy your trip! I live in the Chicago area and have used that cheap F up-fare UK-ORD. Here are some recs
Burgers: Bad Apple (my favorite), Au Cheval is the famous one though
BBQ: Green Street Smoked Meats
Art Institute is very nice! Otherwise for nature you’ll enjoy anything around the lake. If you have time to get out of the city, the Chicago Botanic Garden and Fort Sheridan are enjoyable.